The National Stadium BTS Station is located on Rama 1 Road near the intersection of Phaya Thai Road.
From here it is a 300 meter walk to Jim Thompsons House, or you can get there from Ratchathewi BTS Station but it is about a 500 meter walk from there.
For shopping you have the world famous MBK Center or Mah Boonkrong, also the Siam Paragon, Siam Center, Siam Discovery Center (quicker to walk from the Siam BTS Station), Tokyu Department Store and a Tesco Lotus.
Tourist type places include Siam Ocean World, of which you can read more about here.
For hotels in this area you have the Pathumwan Princess Hotel.